ABSTRACT: The problem of lateral load induced on piles under earthquake has been plaguing professional engineers, geo-technical investigators and researchers alike for quite some time. The normal practice is to ensure that the fixed base shear of column does not exceed the static shear load capacity of piles. The inertial and stiffness effect of pile is usually ignored in dynamic earthquake analysis. The present paper proposes a method where based on modal response or time history analysis pile load may be estimated under earthquake, considering its stiffness, inertia and effect of material and geometric damping properties. The results are then compared with the conventional methods. The effect of partial embedment, a situation that may develop under soil liquefaction during earthquake has also been derived. The pile loads are estimated for two cases: 1) When the structure is a lumped mass having infinite stiffness: like a machine foundation or a heavy short vessel supported directly on pile cap. 2) The superstructure has a finite stiffness and mass like a frame (building /pipe rack etc) The paper also suggests a way of how a geo-technical investigator can estimate rationally the dynamic pile loading with minimum information available at the outset of a project. One of the major advantages of the method is that it does not warrant sophisticated software to be developed for this analysis. A simple spread sheet is sufficient to produce an accurate result.

Introduction

Vibration of piles under lateral load is an important study for piles supporting machines and structures under earthquake loading. In majority of the cases, of all the modes, the lateral vibration is the most critical and often governs the design during an earthquake. Thus, a study of such motion is of paramount importance for piles supporting important installations. A number of researchers have proposed solution to the problem of pile dynamics, namely, Parmelee et al. (1964), Tajimi (1966), Penzien (1970), Novak et al. (1974, 1983), Banerjee and Sen (1987), Dobry and Gazetas (1988) only to name a few. However, most of these solutions are based on harmonic analysis and are valid for the design of machine foundations, where the dynamic stiffness and damping of pile remain frequency dependent. The application of these theories are though well established for design of machine foundations except for an approximate method as proposed by Chandrashekaran (1974) and Prakash (1973), a comprehensive analytical tool to predict the pile response under earthquake load still remains uncertain.

The Proposed Method

The present paper deals with a semi-analytic solution for predicting the lateral load on a pile under earthquake forces. For obtaining the time period vis-a vis the stiffness and mass of the system, one may start with a pile embedded in homogeneous elastic medium under plane strain condition as shown in Figure 1. To start with, the pile is taken as long and slender. Under static condition, the equation of equilibrium in the x-direction is given by: